SIGGRAPH Asia 2010

Diffusion Maps for Edge-Aware Image Editing

The Hebrew University

Abstract:

Edge-aware operations, such as edge-preserving smoothing and edge-aware interpolation, require assessing the degree of similarity between pairs of pixels, typically defined as a simple monotonic function of the Euclidean distance between pixel values in some feature space.
In this work we introduce the idea of replacing these Euclidean distances with diffusion distances, which better account for the global distribution of pixels in their feature space.These distances are approximated using diffusion maps: a set of the dominant eigenvectors of a large affinity matrix, which may be computed efficiently by sampling a small number of matrix columns (the Nystrom method).
We demonstrate the benefits of using diffusion distances in a variety of image editing contexts, and explore the use of diffusion maps as a tool for facilitating the creation of complex selection masks.
Finally, we present a new analysis that establishes a connection between the maximal spatial interaction range between two pixels, and the number of samples necessary for accurate Nystrom approximations.

Supplementary Materials:

It can be difficult to fully appreciate the differences
between the small side-by-side images in the paper. Therefore, in
these supplementary materials we include larger format versions of
the images in the paper, with the ability to easily flip between them.
We also include additional comparisons, examples, and visualizations.
The material is organized in several pages, roughly corresponding to
the figures in the paper.

Note: In order to view these pages properly,
JavaScript must be enabled in your browser. In Internet Explorer, you
may also need to allow blocked active content to run.